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Simplifying 6x2 + -10x + -34 = 0 Reorder the terms: -34 + -10x + 6x2 = 0 Solving -34 + -10x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-17 + -5x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-17 + -5x + 3x2)' equal to zero and attempt to solve: Simplifying -17 + -5x + 3x2 = 0 Solving -17 + -5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.666666667 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '5.666666667' to each side of the equation. -5.666666667 + -1.666666667x + 5.666666667 + x2 = 0 + 5.666666667 Reorder the terms: -5.666666667 + 5.666666667 + -1.666666667x + x2 = 0 + 5.666666667 Combine like terms: -5.666666667 + 5.666666667 = 0.000000000 0.000000000 + -1.666666667x + x2 = 0 + 5.666666667 -1.666666667x + x2 = 0 + 5.666666667 Combine like terms: 0 + 5.666666667 = 5.666666667 -1.666666667x + x2 = 5.666666667 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 5.666666667 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 5.666666667 + 0.6944444447 Combine like terms: 5.666666667 + 0.6944444447 = 6.3611111117 0.6944444447 + -1.666666667x + x2 = 6.3611111117 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 6.3611111117 Calculate the square root of the right side: 2.522124325 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 2.522124325 and -2.522124325.Subproblem 1
x + -0.8333333335 = 2.522124325 Simplifying x + -0.8333333335 = 2.522124325 Reorder the terms: -0.8333333335 + x = 2.522124325 Solving -0.8333333335 + x = 2.522124325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 2.522124325 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 2.522124325 + 0.8333333335 x = 2.522124325 + 0.8333333335 Combine like terms: 2.522124325 + 0.8333333335 = 3.3554576585 x = 3.3554576585 Simplifying x = 3.3554576585Subproblem 2
x + -0.8333333335 = -2.522124325 Simplifying x + -0.8333333335 = -2.522124325 Reorder the terms: -0.8333333335 + x = -2.522124325 Solving -0.8333333335 + x = -2.522124325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -2.522124325 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -2.522124325 + 0.8333333335 x = -2.522124325 + 0.8333333335 Combine like terms: -2.522124325 + 0.8333333335 = -1.6887909915 x = -1.6887909915 Simplifying x = -1.6887909915Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.3554576585, -1.6887909915}Solution
x = {3.3554576585, -1.6887909915}
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